Question

Which table determines a linear function?

Answer 1

From left to right:

Table 1:

Choose two points, for example (0,1) and (2,4), then

`m = 3/2\\y -1 = mx\\y = (3)/(2)x + 1`

Note that (1,2) is not in thhis linear equation. So, the table does not correspond to a linear function. (It does not means that you cannot models with two linear function for example).

Table 2.

Take (0,0), (1,3)

`m = 3/2\\y = 3/2 x`

The points (1,1) and (3,6) is not in this function.

Table 3. Proceed in the same way, and then there are points that cannont models with the same linear function.

Table 4. Take (0,1), (1,3).

`m = 2\\y -1 =2x\\y = 2x +1`

Note that (2,5) and (3,7) lies in this linear function.

So, the answer is the table 4.